Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six

被引：8

作者：

Liu, Zhengwei ^{[1
,2
]}

Palcoux, Sebastien ^{[2
]}

Ren, Yunxiang ^{[3
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Dept Math, Beijing, Peoples R China

[2] Beijing Inst Math Sci & Applicat, Beijing, Peoples R China

[3] Harvard Univ, Dept Phys, Cambridge, MA 02138 USA

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2022年 / 112卷 / 03期

关键词：

Fusion ring; Grothendieck ring; Fusion category; Categorification; Classification; Multiplicity-free;

D O I：

10.1007/s11005-022-01542-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one up to rank six. Among 72 possible fusion rings, 25 ones are filtered out by using categorification criteria. Each of the remaining 47 fusion rings admits a unitary complex categorification. We found 6 new Grothendieck rings, categorified by applying a localization approach of the pentagon equation.

引用

页数：37

共 35 条

[1]

[Anonymous], 2013, ARXIV13052229

[2]

[Anonymous], 2020, SAGEMATH SAGE MATH S

[3] Classification of metaplectic modular categories [J].

Ardonne, Eddy ;

Cheng, Meng ;

Rowell, Eric C. ;

Wang, Zhenghan .

JOURNAL OF ALGEBRA, 2016, 466 :141-146

[4]

Bonderson P. H., 2007, PhD thesis

[5] On the classification of weakly integral modular categories [J].

Bruillard, Paul ;

Galindo, Cesar ;

Ng, Siu-Hung ;

Plavnik, Julia Y. ;

Rowell, Eric C. ;

Wang, Zhenghan .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (06) :2364-2388

[6] Braided Zesting and Its Applications [J].

Delaney, Colleen ;

Galindo, Cesar ;

Plavnik, Julia ;

Rowell, Eric C. ;

Zhang, Qing .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021, 386 (01) :1-55

[7] On braided fusion categories I [J].

Drinfeld, Vladimir ;

Gelaki, Shlomo ;

Nikshych, Dmitri ;

Ostrik, Victor .

SELECTA MATHEMATICA-NEW SERIES, 2010, 16 (01) :1-119

[8] On fusion categories [J].

Etingof, P ;

Nikshych, D ;

Ostrik, V .

ANNALS OF MATHEMATICS, 2005, 162 (02) :581-642

[9]

Etingof P., 2020, COMMUNICATION

[10]

Etingof P., 2021, ARXIV210213239

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